Diffusers play a very important role in the realm of optics. These devices are often used as integral parts of illumination systems for a wide range of optical devices. With the advent of multilayer reflectors, optical systems have been pushing towards ever-shorter wavelengths. Recently, extreme ultraviolet (EUV) wavelength systems have attracted significant interest due to their applicability to next-generation projection lithography for semiconductor manufacturing. It would be highly desirable to have diffusers for this new area of optics. In visible-light systems, diffusers are typically based on rough transmission devices that impart a spatially random phase shift on the light by virtue of the light passing through random lengths of phase shifting material. This is convenient at visible wavelengths because numerous materials, such as glass, exist that provide strong phase shift with negligible attenuation relative to free space. At EUV, however, such materials are hard to find. It is, therefore, preferable to use reflection diffusers at EUV wavelengths. A reflection diffuser at EUV can be, in principle, produced by depositing an EUV reflective multilayer onto a rough substrate. The spatially random surface height acts to impart a random phase shift upon reflection, diffusing the light. To achieve adequate efficiency, however, the roughness of the substrate must be well controlled. Experience has shown that naturally rough substrates do not provide enough control for the fabrication of effective EUV diffusers. Practical EUV diffusers, thus, require the use of engineered random relief substrates. The art is in need of a fabrication method allowing arbitrary random relief substrates to be fabricated for use with EUV diffusers.